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anzhelika [568]
4 years ago
12

Factor the binomial 49x2-4

Mathematics
1 answer:
lutik1710 [3]4 years ago
4 0
Rewrite <span><span>49<span>x2</span></span><span>49<span>x2</span></span></span> as <span><span><span>(<span>7x</span>)</span>2</span><span><span>7x</span>2</span></span>.<span><span><span><span>(<span>7x</span>)</span>2</span><span>−4</span></span><span><span><span>7x</span>2</span><span>-4</span></span></span>Rewrite <span>4</span> as <span><span>2^</span><span>2</span></span>.<span><span><span><span>(<span>7x</span>)^</span>2</span><span>−<span>2^</span></span></span><span><span><span>2</span></span></span></span>Since both terms are perfect squares, factor using the difference of squares formula, 
<span><span><span><span>a^2</span><span>−<span>b^2</span></span></span>=<span><span>(<span>a+b</span>)</span><span>(<span>a<span>−b</span></span>) </span></span></span></span>where <span><span>a=<span>7x </span></span><span>and </span></span><span><span>b=2.</span></span><span><span>(<span><span>7x</span>+2</span>)</span><span>(<span><span>7x</span><span>−2</span></span><span>)</span></span></span>
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